The observations of doubly charmed baryon \(\Xi _{cc}^{++}(ccu)\)  and fully-heavy tetraquark \(X(cc\bar{c}\bar{c})\)  indicate that if the doubly charmed tetraquark state like \((cc\bar{u}\bar{d})\)  exists it should be accessible in \(DD^*\)  final states. Exhilaratingly, the LHCb Collaboration found a very narrow peak near the \(DD^*\)  threshold in the \(D^0D^0\pi ^+\)  invariant mass spectrum recently [1]}. The preliminary results show the quantum number of the state is \(J^P=1^+\)  and the mass is almost 273 keV lower than \(D^0D^{*+}\)  threshold.
On the theoretical side, doubly charmed tetraquark \((cc\bar{u}\bar{d})\)  states are anticipated for more than 40 years and are the prime candidates of tightly bound exotic systems and weakly decaying. The mass spectra and possible decay channels are studied by many groups using quark model-based potential model [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, QCD sum rules [14]}, [15]}, [16]}, [17]}, effective field theory [18]}, [19]}, [20]}, lattice QCD [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]} and so on. Almost all the studies indicate the doubly bottomed tetraquarks \((bb\bar{q}\bar{q})\)  are below the meson-meson thresholds which makes them stable, while the doubly charmed tetraquarks \((cc\bar{q}\bar{q})\)  are almost above the thresholds. And for doubly heavy tetraquarks \(bc\bar{q}\bar{q}\) , some studies [2]}, [30]} suggest \(bc\bar{q}\bar{q}\)  tetraquarks are slightly below the threshold of \(\bar{D}B\)  meson, while others advise their masses are above the threshold [3]}, [6]}, [5]}, [13]}.
In this paper, we use the improved chromomagnetic model (ICMI) [35]}, [36]}, [37]} which includes both chromomagnetic and chromoelectric effects to study the doubly-heavy tetraquark states and want to find new possible stable states.
